By way of example, there are applications in which the logarithm of the magnitude of a complex digital input signal consisting of a real component I and an imaginary component Q must be used to produce, for example, a logarithmically scaled controlled variable. Common practice heretofore has been either to calculate the function value, for example by iterative methods, or to keep the function values in readiness in extensive tables and retrieve them according to the value of the input signal. Calculating function values in real time is so hardware-intensive as to render it ordinarily impracticable. If one table is stored for all the possible values of the input signal, either the storage requirements will be high, or the indices in the table will be so far apart that either the accuracy achieved will be very low or the interpolation method will require much more intensive use of resources to interpolate between indices.
The object on which the present invention is based is to create a method and a device for generating a digital output signal as a mathematical function of a digital input signal, together with a computer program for implementing the method, whose storage requirements for the function table are minimal but by means of which the function values on which the output signal is based can still be determined with high accuracy.
This object is achieved with respect to the methods, devices, and computer programs set forth in greater detail below, and as recited in the claims.
According to the invention, only a compressed argument range of the mathematical function is used, i.e., the range of argument values for which the function is tabulated is sharply limited in comparison to the permissible range of values of the input signal. Within this compressed argument range, the function values can also be tabulated relatively close together to occupy a limited amount of storage space. The level of the input signal is modified, by appropriate amplification or attenuation, in such a way that a signal supplied to the table lies within the compressed argument range in which the mathematical function is tabulated. The amplification or attenuation factor is used to generate a correction signal by means of which the output signal, consisting of the tabulated and potentially interpolated function values, is corrected.
The dependent claims permit advantageous improvements of the invention.